Compound trend renewal process with discounted claims: a unified approach

We derive recursive formulas for the moments of compound trend renewal sums with discounted claims. An integral expression for the moment generating function of this risk process is then obtained, from which particular distribution functions are found. We extend the compound (deterministic) trend renewal process by assuming a stochastic trend, a stochastic force of net interest and a stochastic dependence between the inter-occurrence times and the severities of the claims. Finally, stochastic dominance ordering is also observed between the compound trend renewal process and an associated non-homogeneous Poisson process.